<PAGE>   1





                                 UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                            WASHINGTON, D.C.  20549

                                   FORM 10-Q

/X/          QUARTERLY REPORT PURSUANT TO SECTION 13 OR 15(d)
                   OF THE SECURITIES EXCHANGE ACT OF 1934
              For the quarterly period ended SEPTEMBER 30, 1996

                                     OR

/ /           TRANSITION REPORT PURSUANT TO SECTION 13 OR 15(d) 
                   OF THE SECURITIES EXCHANGE ACT OF 1934
           For the transition period from            to           
                                          ----------    ----------

                       Commission file number 1-10934

                      LAKEHEAD PIPE LINE PARTNERS, L.P.
           (Exact name of registrant as specified in its charter)

           DELAWARE                                           39-1715850     
(State or other jurisdiction of                            (I.R.S. Employer  
incorporation or organization)                            Identification No.)

                              LAKE SUPERIOR PLACE
                            21 WEST SUPERIOR STREET
                             DULUTH, MN  55802-2067
             (Address of principal executive offices and zip code)

                                 (218) 725-0100
              (Registrant's telephone number, including area code)


Indicate by check mark whether the Registrant (1) has filed all reports
required to be filed by Section 13 or 15(d) of the Securities Exchange Act of
1934 during the preceding 12 months (or for such shorter period that the
Registrant was required to file such reports), and (2) has been subject to such
filing requirements for the past 90 days. Yes  X  No    
                                              ---    ---

The Registrant had 20,090,000 Preference Units outstanding as at November 1,
1996.
<PAGE>   2



PART I - FINANCIAL INFORMATION


ITEM 1.  FINANCIAL STATEMENTS



                       LAKEHEAD PIPE LINE PARTNERS, L.P.
                        CONSOLIDATED STATEMENT OF INCOME


<TABLE>
<CAPTION>
--------------------------------------------------------------------------------------------------------------
                                                                   Three months ended        Nine months ended
                                                                      September 30,            September 30,
(unaudited; dollars in millions, except per unit amounts)           1996        1995         1996        1995
--------------------------------------------------------------------------------------------------------------
<S>                                                             <C>          <C>         <C>          <C>
Operating Revenue (Note 3)                                      $   67.9     $   66.2    $   201.8    $  199.8
--------------------------------------------------------------------------------------------------------------
Expenses
  Power                                                             13.6         15.2         44.5        47.6
  Operating and administrative                                      19.5         18.9         49.7        50.5
  Depreciation (Note 7)                                              9.1          9.5         29.0        28.4
  Provision for prior years' rate refunds (Note 3)                   -            -           22.1        22.9
--------------------------------------------------------------------------------------------------------------

                                                                    42.2         43.6        145.3       149.4
--------------------------------------------------------------------------------------------------------------

Operating Income                                                    25.7         22.6         56.5        50.4

Interest Income                                                      2.5          1.8          7.1         5.1

Interest Expense (Note 3)                                          (10.3)        (9.8)       (34.6)      (30.5)

Minority Interest                                                   (0.2)        (0.1)        (0.4)       (0.3)
--------------------------------------------------------------------------------------------------------------

Net Income                                                      $   17.7     $   14.5    $    28.6    $   24.7
==============================================================================================================

Net Income Per Unit (Note 2)                                    $   0.72     $   0.59    $    1.15    $   0.99
==============================================================================================================

Cash Distributions Paid Per Unit (Note 5)                       $   0.64     $   0.64    $    1.92    $   1.92
==============================================================================================================
</TABLE>

See accompanying notes to the consolidated financial statements.


                                      2

<PAGE>   3


                       LAKEHEAD PIPE LINE PARTNERS, L.P.
                      CONSOLIDATED STATEMENT OF CASH FLOWS



<TABLE>
<CAPTION>
--------------------------------------------------------------------------------------------------------------
                                                                                            Nine months ended
                                                                                              September 30,
(unaudited; dollars in millions)                                                             1996       1995
--------------------------------------------------------------------------------------------------------------
<S>                                                                                      <C>          <C>
Operating Activities
  Net income                                                                             $    28.6    $   24.7
  Adjustments to reconcile net income to
    cash provided from operating activities:
       Depreciation                                                                           29.0        28.4
       Accrued rate refunds and related interest                                              41.5        41.0
       Other                                                                                  (0.2)        0.6
       Changes in operating assets and liabilities:
          Accounts receivable and other current assets                                        (0.4)        2.1
          Materials and supplies                                                               0.1        (0.5)
          General Partner and affiliates                                                       0.4          -
          Accounts payable and accrued liabilities                                             2.8       (13.0)
          Interest payable                                                                     5.9         7.6
          Property and other taxes                                                            (2.8)        1.1
--------------------------------------------------------------------------------------------------------------

                                                                                             104.9        92.0
--------------------------------------------------------------------------------------------------------------

Investing Activities
  Additions to property, plant and equipment                                                 (52.5)      (23.8)
  Short-term investments, net                                                                 11.1        (9.6)
--------------------------------------------------------------------------------------------------------------

                                                                                             (41.4)      (33.4)
--------------------------------------------------------------------------------------------------------------

Financing Activities
  Issuance of variable rate financing                                                         41.0        14.0
  Distributions to partners                                                                  (47.1)      (47.1)
  Minority interest                                                                           (0.5)       (0.5)
--------------------------------------------------------------------------------------------------------------

                                                                                              (6.6)      (33.6)
--------------------------------------------------------------------------------------------------------------

Increase in Cash and Cash Equivalents(1)                                                      56.9        25.0

Cash and Cash Equivalents at Beginning of Period                                              77.0        42.0
--------------------------------------------------------------------------------------------------------------
Cash and Cash Equivalents at End of Period                                               $   133.9    $   67.0
==============================================================================================================
</TABLE>


(1) Cash equivalents are defined as all highly marketable securities with a
    maturity of three months or less when purchased.  Short-term investments are
    those marketable securities which have a maturity of more than three months
    when purchased.

See accompanying notes to the consolidated financial statements.



                                      3
<PAGE>   4


                       LAKEHEAD PIPE LINE PARTNERS, L.P.
                  CONSOLIDATED STATEMENT OF FINANCIAL POSITION


<TABLE>
<CAPTION>
--------------------------------------------------------------------------------------------------------------
                                                                               September 30,      December 31,
(unaudited, except for December 31, 1995; dollars in millions)                          1996              1995
--------------------------------------------------------------------------------------------------------------
<S>                                                                                 <C>              <C>
                                                             ASSETS
Current Assets
 Cash and cash equivalents                                                          $ 133.9            $  77.0
 Short-term investments                                                                64.6               75.7
 Accounts receivable and other current assets                                          26.9               26.5
 Materials and supplies                                                                 5.3                5.4
--------------------------------------------------------------------------------------------------------------

                                                                                      230.7              184.6
--------------------------------------------------------------------------------------------------------------

Deferred Charges and Other Assets                                                       6.1                5.5
--------------------------------------------------------------------------------------------------------------

Property, Plant and Equipment
 At cost                                                                              861.0              808.8
 Accumulated depreciation                                                            (112.4)             (83.7)
--------------------------------------------------------------------------------------------------------------
                                                                                      748.6              725.1
--------------------------------------------------------------------------------------------------------------

                                                                                    $ 985.4            $ 915.2
==============================================================================================================



                                                 LIABILITIES AND PARTNERS' CAPITAL
Current Liabilities
 Due to General Partner and affiliates                                              $   1.7            $   1.3
 Accounts payable and accrued liabilities                                              16.0               13.2
 Interest payable                                                                       8.4                2.5
 Property and other taxes                                                               9.4               12.2
 Accrued rate refunds and related interest (Note 3)                                   120.0               78.5
--------------------------------------------------------------------------------------------------------------

                                                                                      155.5              107.7
Long-Term Debt (Note 6)                                                               436.0              395.0
Minority Interest                                                                       1.3                1.4
Contingencies (Note 4)
--------------------------------------------------------------------------------------------------------------

                                                                                      592.8              504.1
--------------------------------------------------------------------------------------------------------------

Partners' Capital
 General Partner                                                                        1.6                1.5
 Common Unitholder (units issued - 3,912,750)                                          20.1               21.7
 Preference Unitholders (units issued - 20,090,000)                                   370.9              387.9
--------------------------------------------------------------------------------------------------------------

                                                                                      392.6              411.1
--------------------------------------------------------------------------------------------------------------

                                                                                    $ 985.4            $ 915.2
==============================================================================================================
</TABLE>



See accompanying notes to the consolidated financial statements.


                                      4
<PAGE>   5


                       LAKEHEAD PIPE LINE PARTNERS, L.P.
                  CONSOLIDATED STATEMENT OF PARTNERS' CAPITAL



<TABLE>
<CAPTION>
-------------------------------------------------------------------------------------------------------------
(unaudited, except for December 31, 1995;            General          Common       Preference
 dollars in millions)                                Partner      Unitholder      Unitholders           Total
-------------------------------------------------------------------------------------------------------------
<S>                                              <C>            <C>            <C>               <C>
Partners' Capital at December 31, 1995             $    1.5       $    21.7      $     387.9       $    411.1

Net Income Allocation                                   1.1             5.9             21.6             28.6

Distributions to Partners                              (1.0)           (7.5)           (38.6)           (47.1)
-------------------------------------------------------------------------------------------------------------
Partners' Capital at September 30, 1996            $    1.6       $    20.1      $     370.9       $    392.6
=============================================================================================================
</TABLE>

See accompanying notes to the consolidated financial statements.


           NOTES TO THE CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

1.   Basis of Presentation

     The accompanying unaudited consolidated financial statements have been
     prepared in accordance with United States generally accepted accounting
     principles for interim financial information and with the instructions to
     Form 10-Q and Rule 10-01 of Regulation S-X.  Accordingly, they do not
     include all the information and footnotes required by generally accepted
     accounting principles for complete financial statements.  In the opinion
     of management, they contain all adjustments, consisting of normal
     recurring adjustments, and non-recurring adjustments to both the first
     quarter of 1995  reflecting a 1995 Federal Energy Regulatory Commission
     ("FERC") decision and the first quarter of 1996 reflecting a tariff rate
     agreement approved by the FERC in October 1996, which management considers
     necessary to present fairly the financial position as at September 30,
     1996 and December 31, 1995; the results of operations for the three month
     and nine month periods ended September 30, 1996 and 1995; and cash flows
     for the nine month periods ended September 30, 1996 and 1995.  The results
     of operations for the nine months ended September 30, 1996 should not be
     taken as directly indicative of the results to be expected for the full
     year.  The interim financial statements should be read in conjunction with
     the Partnership's consolidated financial statements and notes thereto
     presented in the Partnership's 1995 Annual Report on Form 10-K.  Certain
     comparative amounts are reclassified to conform with the current year's
     financial statement presentation.

2.   Net Income Per Unit

     Net income per unit is computed by dividing net income, after deduction of
     the General Partner's allocation, by the  number of Preference and Common
     Units outstanding.



                                      5
<PAGE>   6


3.   Accrued Rate Refunds and Related Interest

     On October 16, 1996, the FERC approved a July 1996 agreement between the
     Partnership and customer representatives on all outstanding contested
     tariff rates.  The agreement results in an approximate tariff rate
     reduction of 6% and total rate refunds and related interest of $120.0
     million through an effective date of October 1, 1996.  Of that total,
     approximately $37 million will be refunded in a lump sum in the fourth
     quarter of 1996, with the remainder (including additional carrying
     charges) repaid through reduced tolls over a three-year period commencing
     November 1, 1996.  The Partnership has accrued rate refunds and related
     interest of $120.0 million through September 30, 1996, of which $41.5
     million has been accrued this year to reflect the agreement. Of the amount
     accrued in 1996, rate refunds related to 1996 ($10.8 million) have reduced
     Operating Revenue, with the prior years' portion  ($22.1 million)
     separately stated as a Provision for Prior Years' Rate Refunds.  Accrued
     interest ($8.6 million, of which $3.2 million is related to prior years)
     has been reflected in Interest Expense.

4.   Environmental Contingencies

     The Partnership is subject to federal and state laws and regulations
     relating to the protection of the environment.  Environmental risk is
     inherent to liquid pipeline operations and the Partnership could, at
     times, be subject to environmental cleanup and enforcement actions.  The
     General Partner manages this environmental risk through appropriate
     environmental policies and practices to minimize the impact to the
     Partnership.  To the extent that the Partnership is unable to recover
     environmental costs in its rates or through insurance, the General Partner
     has agreed to indemnify the Partnership from and against any costs
     relating to environmental liabilities associated with the Lakehead System
     prior to its transfer to the Partnership in 1991.  This excludes any
     liabilities resulting from a change in laws after such transfer.  The
     Partnership continues to voluntarily investigate past leak sites for the
     purpose of assessing whether any remediation is required in light of
     current regulations, and to date no material environmental risks have been
     identified.

5.   Cash Distribution

     On October 16, 1996, the Board of Directors of the General Partner
     announced an increase of $0.04 per unit in the quarterly cash
     distribution. Accordingly, the distribution declared for the quarter ended
     September 30, 1996 was $0.68 per unit.  The distribution will be made on
     November 14, 1996 to unitholders of record October 31, 1996.

6.   Debt

     In September 1996, the Partnership executed an Amended and Restated
     Revolving Credit Facility with its banks in the amount of $205.0 million.
     The terms of the amendment provide for the maturity date to be extended to
     at least September 2001 from the previous maturity date of 1999. On an
     annual basis, the banks may provide a Notice of Non-Continuation which, if
     exercised, would establish the maturity date at four years from the next
     anniversary date of the facility.  If such notice is not provided by the
     banks, the facility's term will be extended one year.  The facility
     currently carries a fee of 0.085% per annum on the entire $205.0 million,
     plus credit spreads on drawn amounts.  The facility fee and credit spread
     are based on the type of collateral provided for the loans and certain
     cash flow to interest expense ratios.  The total amount drawn under the
     facility by the Partnership was $126.0 million at September 30, 1996.


                                      6
<PAGE>   7


7.  Depreciation Rates

    Effective July 1, 1996, the Partnership revised the estimated service lives
    of its property, plant and equipment to better represent the economic life
    of its pipeline system.  The change in estimated service lives had the
    following impact on depreciation rates:

<TABLE>
<CAPTION>
                                                                                   Average
     Type of Property                                                        Depreciation Rates         
     ----------------                                                -----------------------------------
     <S>                                                                     <C>
     Rights-of-way                                                            3.6% (from 3.95%)
     Pipeline                                                                4.09% (from 3.95%)
     Pumping equipment, buildings and tanks                                  4.42% (from 6.82%)
     Vehicles, office and communications equipment                           12.51% (from 7.24%)
</TABLE>

     This change increased net income by $0.9 million, or $0.03 per unit, for
     both the nine month and three month periods ended September 30, 1996.



ITEM 2.   MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION AND
          RESULTS OF OPERATIONS


On October 16, 1996, the Board of Directors of the General Partner increased
the quarterly cash distribution to $0.68 per unit from $0.64 per unit.  This
increase, the second since the Partnership's inception, raises the annual
distribution rate to $2.72 per unit and is the result of continued earnings
growth and removal of the uncertainty relating to the Partnership's tolls.  In
recent years, the Partnership has followed a conservative distribution policy
pending settlement of its rate refund obligations.  As a result of the
resolution of the Partnership's refund obligations and future rates, the
Partnership is now in a position to move gradually toward a more typical master
limited partnership distribution pay-out.  Following this increase, the pay-out
ratio will still be more conservative than average, in anticipation of
significant investment during 1997 and 1998 for expansion of the pipeline.
However, the General Partner believes that this investment will result in
increased cash flow and will enhance the Partnership's future distribution
capability.

On October 16, 1996, the FERC approved the July 1996 agreement between the
Partnership and customer representatives on all outstanding contested tariff
rates.  For additional details, reference should be made to Part I, Item 1,
"Notes to the Consolidated Financial Statements", Note 3.

RESULTS OF OPERATIONS

NINE MONTHS ENDED SEPTEMBER 30, 1996 COMPARED WITH NINE MONTHS ENDED SEPTEMBER
30, 1995

The Partnership continues to match the strong operational performance of last
year as deliveries averaged 1,421,000 barrels per day for the first nine months
of 1996, up slightly from the 1,405,000 barrels per day averaged for the same
period of 1995. System utilization, measured in barrel miles, decreased 1% from
the first nine months of last year, reflecting a higher proportion of shorter
haul deliveries to the significant Midwest markets served by the Partnership.

Net income for the nine months ended September 30, 1996 was $28.6 million, or
$1.15 per unit, an increase of $3.9 million, or $0.16 per unit, over the first
nine months of 1995.  Net income is skewed in both periods by the rate refunds
and related interest recorded in response to various tariff rate regulatory
developments.  As such, the following "Recalculated Operating Results" section
presents recalculated financial information to facilitate the comparison of
operating results.  This information



                                      7

<PAGE>   8

includes the impact of the tariff rate agreement on the periods presented and
excludes any amounts related to prior years.

Recalculated Operating Results
<TABLE>
<CAPTION>
                                                        (dollars in millions, except per unit amounts)
                                                               Nine Months Ended September 30,
                                                                1996                    1995 
                                                                ----                    -----
             <S>                                            <C>                      <C>
             Operating Revenue                              $  201.8                 $  199.8
             Operating Expenses                               (123.2)                  (126.5)
             Interest Income                                     7.1                      5.1
             Interest Expense                                  (31.4)                   (29.0)
             Minority Interest                                  (0.6)                    (0.6)
                                                            --------                 -------- 
             Net Income                                     $   53.7                 $   48.8 
                                                            ========                 ========
             Net Income per Unit                            $   2.18                 $   1.99 
                                                            ========                 ========
</TABLE>

Recalculated net income for the nine months ended September 30, 1996 was $4.9
million, or $0.19 per unit, higher than the recalculated net income for the
same period of last year.  A combination of higher operating revenue, lower
total operating expenses and greater interest income, partially offset by
higher interest expense, led to the increase.

Recalculated operating revenue was up slightly over 1995 primarily due to a
higher proportion of heavy crude oil deliveries (up 27% to 447,000 barrels per
day).  Due to its higher viscosity, which requires more horsepower to pump, the
tariff rate for heavier crude oil is greater than that for lighter crude oils.
The Partnership's current tariff rate for heavy crude oil deliveries to the
Chicago area is approximately 10% to 18% higher than that for lighter crude
oils.

Recalculated operating expenses for the first nine months of 1996 were $3.3
million less than the same period of 1995.  This is primarily due to lower
power costs and oil losses, partially offset by higher depreciation.
Efficiencies gained from the Partnership's ongoing power cost management
initiative, partially offset by the transportation of greater amounts of heavy
crude oil, led to the decrease in power costs.  Oil losses are impacted by
operational considerations, including changing customer delivery requirements,
and the volatility of crude oil prices, resulting in variances in the level of
losses from period to period.  Higher depreciation corresponded to the growth
in property, plant and equipment, partially offset by new depreciation rates
effective July 1, 1996 (for additional details, reference should be made to
Part I, Item 1, "Notes to the Consolidated Financial Statements", Note 7).

Interest income increased due to higher investment balances.  Recalculated
interest expense increased due to higher accrued rate refund balances and
additional borrowings made under the Partnership's Credit Facility to finance
enhancement capital expenditures.

THREE MONTHS ENDED SEPTEMBER 30, 1996 COMPARED WITH THREE MONTHS ENDED
SEPTEMBER 30, 1995

Net income for the three months ended September 30, 1996 was $3.2 million, or
$0.13 per unit, higher than the same period of last year, primarily due to
higher operating revenue and lower total operating expenses.  Operating revenue
for the third quarter of 1996 was up $1.7 million, or 3%, from 1995's third
quarter primarily due to a higher proportion of heavy crude oil deliveries.
Total operating expenses for the three months ended September 30, 1996 were
$1.4 million less than the corresponding period in 1995, primarily due to lower
power costs and depreciation. Efficiencies gained from the Partnership's
ongoing power cost management initiative, partially offset by the
transportation of greater amounts of heavy crude oil, led to the decrease in
power costs.  Despite the growth in property, plant and equipment, depreciation
decreased as a result of the new depreciation rates effective July 1, 1996.



                                      8
<PAGE>   9

LIQUIDITY AND CAPITAL RESOURCES

At September 30, 1996, cash, cash equivalents and short-term investments
totaled $198.5 million, up $45.8 million since December 31, 1995, as cash
generated from operating activities and borrowings exceeded cash required for
distributions and capital expenditures.  Of this $198.5 million, $17.0 million
($0.68 per unit) was set aside for the cash distribution payable November 14,
1996 with the remaining $181.5 million available for rate refunds, capital
expenditures, distributions or other business needs.

Cash flow from operating activities totaled $104.9 million for the nine months
ended September 30, 1996, an increase of $12.9 million from the corresponding
1995 period.  This was primarily due to lower working capital cash requirements
resulting from timing differences in the payment of accrued obligations.

Capital expenditures to September 30, 1996 totaled $52.5 million, and are
expected to total approximately $85 million for the entire year.  The majority
of this year's capital expenditures are for the Partnership's 1996 system
expansion. This expansion will increase delivery capacity into Chicago area
markets by up to 120,000 barrels per day at a cost of approximately $65
million.  Approximately 40,000 barrels per day of this added capacity will be
required to offset the effects of moving increased volumes of heavy crude oil,
which can lower system delivery capability.  Capital expenditures in 1996 are
being financed with internally-generated cash and borrowings under the Credit
Facility.

Right-of-way acquisition and environmental permitting work has begun for the
Partnership's additional expansion program which consists primarily of a new
450-mile 24-inch pipeline from Superior, Wisconsin to the Chicago, Illinois
area.  This expansion will increase delivery capacity by approximately 170,000
barrels per day to important U.S. Midwest markets at an approximate cost of
$300 million, with completion planned for the second half of 1998.  It is
anticipated that this expansion, which complements an expansion in Canada on
the Interprovincial Pipe Line system, will be financed with internally-
generated cash, borrowings and the proceeds from additional equity issuances.


PART II - OTHER INFORMATION

ITEM 1.  LEGAL PROCEEDINGS

On June 27, 1996, the Partnership filed  a petition for review to the U.S.
Court of Appeals for the District of Columbia Circuit of the June 1995 FERC
decision (Opinion No. 397) and the related May 17, 1996 Opinion No. 397-A.  The
Canadian Association of Petroleum Producers and the Alberta Department of
Energy filed a similar petition for review on May 28, 1996.  These petitions
will now be withdrawn in light of the FERC's October 16, 1996 approval of the
tariff rate agreement.


ITEM 6.  EXHIBITS AND REPORTS ON FORM 8-K

a)  Exhibits

    Exhibit 27  Financial Data Schedule as of and for the nine months ended
    September 30, 1996.

b)  Reports on Form 8-K

    No reports on Form 8-K were filed during the quarter ended September 30,
    1996.


                                      9
<PAGE>   10



                                   SIGNATURE

Pursuant to the requirements of the Securities Exchange Act of 1934, the
Registrant has duly caused this report to be signed on its behalf by the
undersigned thereunto duly authorized.




                                        LAKEHEAD PIPE LINE PARTNERS, L.P.
                                                  (Registrant)

                                By:    Lakehead Pipe Line Company, Inc.
                                       as General Partner





                                                 /s/ S.Q. DeVinck 
                                       ---------------------------------------- 
                                                     S.Q. DeVinck
                                                  Chief Accountant
                                              (Principal Financial and
                                                 Accounting Officer)





                                                   November 8, 1996



                                      10